GRTeclyn

MHDueT

UKNR CCP

• Numerical Relativity is an area of research that uses numerical methods to find and investigate solution to Einstein’s equation of General Relativity (and other modified theories of gravity),

  \[ \underbrace{G_{ab}}_{\text{curvature}} + \underbrace{\Lambda g_{ab}}_{\text{cosmological constant}} = \underbrace{8\pi T_{ab}}_{\text{energy-momentum tensor}}. \]

• We recast the equations into a set of coupled non-linear hyperbolic PDEs with elliptic constraints that we solve for the initial data.

• Common problems include compact object binaries (black holes, neutron stars, more exotic objects) but NR is also used to study cosmological problems and perform “numerical experiments” for fundamental physics.

• We are often interested in the gravitational waves (GWs) emitted in a simulation, particularly in the astrophysical compact binary case.

• Discretization:
  • Finite differences
    • Cell-centered
    • Vertex/node-centered
  • Finite volume (for fluids)
  • Spectral methods
  • Discontinuous Galerkin (DG) methods
• Finite-difference mesh refinement:
  • Block-structured AMR
    • “Moving boxes” for compact object binaries
    • More adaptive for more exotic spacetimes
  • Oct-tree AMR

• Method of lines
  • Fourth order Runge-Kutta time integration
  • Fourth or sixth-order spatial discretization
• Kreiss-Oliger dissipation
• Boundary conditions:
  • Outgoing radiation (Sommerfeld)
  • Symmetric/reflective
  • Extrapolating
  • Multipatch approaches: separate (e.g. spherical) outer grids

Oct-tree AMR

• GRAthena++
• Gmunu
• Dendro-GR
• GRAMSES

[Pseudo-]spectral/DG codes

• SpEC/SpECTRE
• bamps
• SFINGE

Other

• SENR/NRPy+

Block-structured AMR

• Cactus/Einstein Toolkit\(^{\dagger}\)
  • McLachlan, LazEv, Maya, Lean, Canuda, …
• BAM
• PAMR/AMRD libraries
• Hahndol/PARAMESH
• HAD
• CosmoGRaPH
• Simflowny/MHDueT\(^{\dagger}\)
• GRChombo/GRTeclyn\(^{\dagger}\)

• GRTeclyn is an in-development port of GRChombo (previously built on the Chombo libraries) to AMReX.
• “Teclyn” is Welsh for “tool”.
• Features
  • Amr based
  • Cell-centered but finite-difference rather than finite-volume
    • Fourth-order cell-centered interpolator from coarse to fine (CellQuartic)
    • Fourth-order interpolation from fine to coarse
  • Fourth-order Runge-Kutta time integration
  • Currently, just BinaryBH example which evolves black-hole binaries.
  • Designed to be flexible and easy to adapt to new problems.

• Black-hole puncture tracking.
  • Allows us to track the “centres” of black hole during the simulation
  • Uses AMReX’s particle infrastructure
  • Typically 2 BHs so just 2 puncture particles so maybe overkill
  • Good experience for future particle use
• AMD MI300A hackathon
  • Lots of variables so high register pressure in RHS kernels
  • Legacy complicated data structure from GRChombo increases this
  • Refactoring led to a ~2x speedup in RHS kernels (~40% overall) on AMD MI300A APUs.
• Currently working on adding support for basic matter.

• MHDueT is a code that is automatically generated using the Simflowny infrastructure.
• Previously used the SAMRAI library.
• Features
  • AmrCore based.
  • Mostly node-centered
    • Fifth order polynomial interpolation from coarse to fine
  • Custom fourth order Runga-Kutta time integration
  • Supports Magnetohydrodynamics (MHD)
    • High resolution shock capturing with WENO reconstruction
    • Arbitrary EOS via HDF5 tabulated input
  • Can simulate binaries of boson stars, neutron stars, black holes and more.
  • Auto-generated using Simflowny infrastructure to allow minimal user programming.